Resisting moment in precast concrete channel rating

[PMcGG]

I am doing a load rating analysis on Concrete channel bridge made in the 70's. I have not ratede one of these before and the rating method I am using has a variable that I am not familiar with. I was wondering if anyone else knew what it was.

The equation for the resisting moment in the channel is:

RM= As(fi)jd/12
RM= Resisting moment "ft-kip"
As= Area of steel "in^2"
fi= steel strength "psi"
d= effective depth of channel "in"
j= ???

j has no units so I was wondering what constant would be in this equation.

 

[Lion06]

the term jd is used to represent the distance from the steel to the centroid of the compression block. It is the same as (d-a/2) for more modern reinforced concrete.
That term j comes up often in ASD design of concrete and in masonry design.
jd = d-a/2

 

[Lion06]

Check out an old RC design book (ASD) for further discussion on exactly what j is. You can also look in NCMA TEK Notes on ASD Design of Masonry. I believe they are identical, they are just found using different properties for masonry or concrete.
I have an old RC Book called "The Design of Reinforced Concrete Structures" by Dean Peabody. It was printed in 1951.

 

[hokie66]

Comments above are on the right track, except that the compression block in Working Stress Design was assumed to be triangular, so jd is d-kd/3, where k is the depth of the triangular compression block.

To make the units work correctly, the steel strength in the equation should be in ksi rather than psi.

Another good reference, not quite so old, is Winter et al, "Design of Concrete Structures", Seventh Edition. This textbook contains both WSD and USD, and was published at the time of the introduction of ACI318-63, which was the first code to adopt USD as the basic design philosophy, why still recognizing WSD as a design option.